Common Core Standard HSF-BF.B.4 Questions

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Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a

Find the inverse of [math]f(x) = x[/math].

[math]f^{-1}(x) = x[/math]
[math]f^{-1}(x) = y[/math]
[math]f^{-1}(x) = 1[/math]
[math]f^{-1}(x) = 1/x[/math]

Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b

This question is a part of a group with common instructions. View group »

When finding [math]h(x)[/math], what is the importance of the domain?

It has no special importance.
It shows that, even though [math]h(x)[/math] and [math]h_2(x)[/math] seem to be the same function, they have different domains.
It is necessary to see that the domain is all real numbers because the domain of inverse functions, when composed with the original function, needs to be all real numbers.
It means that the absolute value sign can be dropped, since the domain is zero and positive numbers, so the function simply becomes [math]x[/math].

Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4c

If [math]f(x)[/math] is the function in the following graph, what is the value of [math]f^{-1}(0) ?[/math] Assume that the horizontal axis represents [math]x[/math] values and the vertical axis [math]y[/math] values.

-1
0
1
This value does not exist.

Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d

Let [math]f(x) = 3(x-5)^2[/math]. Which of the following domain restrictions makes [math]f(x)[/math] invertible and ensures that [math]f^{-1}(x)[/math] has no maximum value?

[math]x>0[/math]
[math]x>5[/math]
[math]x<5[/math]
[math]x<-5[/math]

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a

Find the inverse of the following function. [math]f(x) = 4x^3 + 2[/math]

[math]f^{-1}(x) = (x^3-2)/4[/math]
[math]f^{-1}(x) = (root[3](x) - 2)/4[/math]
[math]f^{-1}(x) = root[3]((x-2)/4) [/math]
[math]f^{-1}(x) = root[3](x-2)/4[/math]

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b

If [math]f(x) = 3e^(x+2)[/math] and [math]g(x) = ln(x/3)-2[/math], is [math]g(x)[/math] the inverse of [math]f(x) ?[/math] Verify using composition of functions.

Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4c

Let [math]f(x)[/math] be the function in the graph below. What is the approximate value of [math]f^{-1}(1) ?[/math] Assume that the scale on the x- and y-axes is one unit.

-1
-0.75
0
2

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a

What is the inverse of [math]f(x) = 3/(x-1) ?[/math]

[math]f^{-1}(x) = (x+1)/3[/math]
[math]f^{-1}(x) = (x+3)/x[/math]
[math]f^{-1}(x) = 3/(x+1)[/math]
[math]f^{-1}(x) = 4/x[/math]

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b

Using composition of functions, is [math]f(x) = 5root[3](8x-1)[/math] the inverse of [math]x^3/125 + 1/8[/math].

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4c

If [math]f(x)[/math] is the exponential function in the graph below, what is the approximate value of [math]f^{-1}(-1) ?[/math] Assume that the scale on the x- and y-axes is one unit.

0.25
0
5.25
This value does not exist.

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a

Find the inverse of the following function. [math]f(x) = 3^{9x-5}[/math]

[math]f^{-1}(x) = log_3(1/9 x + 5)[/math]
[math]f^{-1}(x) = log_3(x/9) + 5[/math]
[math]f^{-1}(x) = log_3(x+5)/9[/math]
[math]f^{-1}(x) = (log_3(x) + 5)/9[/math]

Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4c

Some of the values of [math]f(x)[/math], an invertible function, are given in the following table. What is the value of [math]f^{-1}(1) ?[/math]

[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math]	[math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] 1 [/math]	[math] 8.9 [/math]
[math] 2 [/math]	[math] 5.3 [/math]
[math] 3 [/math]	[math] 3 [/math]
[math] 4 [/math]	[math] 1 [/math]
[math] 5 [/math]	[math] -7.5 [/math]

8.9
1
-7.5
4

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4c

Let [math]f(x)[/math] be the logarithmic function in the graph below. Using the information in the graph, what is the approximate value of [math]f^{-1}(3) ?[/math] Assume that the scale on the x- and y-axes is one unit.

Not enough information given in the graph to determine this value.
This value does not exist.
0.5
0.01

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a

If [math]f(x) = log_4(3x-1) + 10[/math], what is the inverse of this function?

[math]f^{-1}(x) = (4^(x-10)+1)/3[/math]
[math]f^{-1}(x) = 4(x/3 + 1) - 10[/math]
[math]f^{-1}(x) = 1/3 (4^x -9)[/math]
[math]f^{-1}(x) = 4^((x-10)/3 + 1)[/math]

Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4c

Find the value of [math]f^{-1}(-5.5)[/math], given the values of [math]f(x)[/math] in the following table. Assume that [math]f(x)[/math] has an inverse.

[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math]	[math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] -6 [/math]	[math] -20.5 [/math]
[math] -5.5 [/math]	[math] -11.5 [/math]
[math] -5 [/math]	[math] -5.5 [/math]
[math] -4.5 [/math]	[math] -3.5 [/math]
[math] -4 [/math]	[math] -1.5 [/math]

-5
-11.5
-3.5
-5.5

Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4c

Given the graph below of the logarithmic function [math]f(x)[/math], what is the approximate value of [math]f^{-1}(0.5) ?[/math] Assume that the scale on the x- and y-axes is one unit.

3
0
0.5
This value does not exist.

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a

Find the inverse. [math]f(x) = 1/5 x^3[/math]

[math]f^{-1}(x) = 5root[3](x)[/math]
[math]f^{-1}(x) = root[3](5x)[/math]
[math]f^{-1}(x) = root[3](1/5 x)[/math]
[math]f^{-1}(x) = 1/5root[3](x)[/math]

Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4c

What is the value of [math]f^{-1}(6)[/math], given the following table? Assume that [math]f(x)[/math] has an inverse.

[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math]	[math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] 1/36 [/math]	[math] 6 [/math]
[math] 1/6 [/math]	[math] 10 [/math]
[math] 1 [/math]	[math] 23 [/math]
[math] 6 [/math]	[math] 54 [/math]
[math] 36 [/math]	[math] 103 [/math]

[math]10[/math]
[math]1/36[/math]
[math]54[/math]
It cannot be determined with the information given.

Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4c

Given the function [math]f(x)[/math] in the following graph, what is the approximate value of [math]f^{-1}(4) ?[/math] Assume that the scale on the x- and y-axes is one unit.

2
1.5
-0.1
Not enough information given in the graph to determine this.

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a

Find the inverse. [math]f(x) = (x-8)/(x+1)[/math]

[math]f^{-1}(x) = (x-1)/(x+8)[/math]
[math]f^{-1}(x) = -9/(x+1)[/math]
[math]f^{-1}(x) = (-x-8)/(x-1)[/math]
[math]f^{-1}(x) = (x-8)/x[/math]

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