Common Core Standard HSF-BF.B.4 Questions

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

Match each function with its inverse.

__	$f(x) = 3 ln(x+2)$	A.	$f^{-1} (x) = e^(x//3) -2$
__	$f(x) = e^(5x+2)$	B.	$f^{-1} (x) = (ln(x)-2)/5$
__	$f(x) = log(3x)/2$	C.	$f^{-1} (x) = log(x-5) + 2$
__	$f(x) = 10^{x-2} + 5$	D.	$f^{-1} (x) = 10^{2x}/3$

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

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Find

$h_2(x) = g(f(x))$ and state its domain.

$h_2(x) = x, \ \ x>=0$
$h_2(x) = |x|, \ \ RR$
$h_2(x) = x, \ \ RR$
$h_2(x) = |x|, \ \ x<=0$

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

Let

$f(x)$ be the function in the graph below. Assume that the horizontal axis represents

$x$ values and the vertical axis

$y$ values. What is the value of

$f^{-1}(2) ?$

$-2$
$1$
$2$
$4$

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

For the absolute value function

$f(x)$ pictured in the graph, which of the following domain restrictions would make it invertible? There may be more than one correct answer. Assume that the x- and y-axes have a scale of one unit.

$x>=1$
$x<=0$
$x<0$
$x<-3$

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

The following table represents h(x):
Find h⁻¹(6).

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

Find h(x) = f(g(x)).

h(x) = x², ℝ
h(x) = |x|, ℝ
h(x) = x⁴, ℝ
h(x) = x², x ≥ 0

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

Find h(x) = f(g(x)) and its domain.

h(x) = x, x ≠ 0
h(x) = 1/x², x ≠ 0
h(x) = x, ℝ
h(x) = 1/x, x ≠ 0

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

Find the inverse of the function

$f(x) = 3x-2$ .

$f^{-1}(x) = 1/3 x + 2$
$f^{-1}(x) = x +2$
$f^{-1}(x) = x + 2/3$
$f^{-1}(x) = 1/3 x + 2/3$

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

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$g(x)$ the inverse of

$f(x)?$ Explain.

Yes, since both $h(x)$ and $h_2(x)$ are equal to $x$ .
No, because the domain of $h(x)$ and $h_2(x)$ are different.
No, because $h(x) != x$ .
No, because $h_2(x) != x$ .

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

$f(x)$ is the function in the graph below, what is

$f^{-1}(-2) ?$ Assume that the horizontal axis represents

$x$ values and the vertical axis

$y$ values.

$2$
$1$
$-1$
$4$

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

Given the function

$f(x) = 2x^2 + 28x + 90$ , which of the following restrictions on the domain of

$f(x)$ would make it invertible? There may be more than one correct answer.

$x < 90$
$x >= -8$
$x < -7$
$x < 0$

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

Find the inverse of

$f(x) = (x - 4)/5$ .

f⁻¹(x) = 5x - 4
f⁻¹(x) = 5x + 4
$f⁻¹(x) = (x + 4)/5$
$f⁻¹(x) = (x - 5)/4$

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

Find h₂(x) = g(f(x)) for f(x) = |x| and g(x) = x².

h₂(x) = x², ℝ
h₂(x) = |x|, ℝ
h₂(x) = x⁴, ℝ
h₂(x) = x², x ≥ 0

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

$g(x) = 1/x$ the inverse of

$f(x) = 1/x$ ?

Yes, because h(x) = h₂(x) = x
No, because f(g(0)) is undefined
Only for x > 0
No, because their ranges differ

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

Find the inverse of

$f(x) = x$ .

$f^{-1}(x) = x$
$f^{-1}(x) = y$
$f^{-1}(x) = 1$
$f^{-1}(x) = 1/x$

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

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When finding

$h(x)$ , what is the importance of the domain?

It has no special importance.
It shows that, even though $h(x)$ and $h_2(x)$ 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 $x$ .