Common Core Standard HSF-BF.B.4b Questions

Select All Questions

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

f(x) = 5 − 3x,

$g(x) = (5 − x)/3$ . Find f(g(x)).

x
5 − x
x - 3
-3x

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 »

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

For

$f(x) = (5-x)/(3x)$ and

$g(x) = 5/(3x+1)$ verify if g = f⁻¹.

True
False

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

Given

$f(x) = (2x+3)/(x-1)$ and

$g(x) = (x+3)/(x-2)$ , are they inverses?

True
False

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

Why is the domain of h(x) = f(g(x)) restricted in exponential-logarithmic compositions?

Because ln(x) is only defined for x > 0
Because eˣ cannot output negative values
Both a and b
Neither - the domain is always ℝ

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

Given

$f(x) = (2eˣ-3)/(eˣ+4)$ and

$g(x) = ln[(3+4x)/(2-x)]$ , is g = f⁻¹?

True
False

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

Given f(x) = (x + 5)² (x ≥ -5) and g(x) = √x - 5, is g the inverse of f?

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

$f(x) = log_2(x)$ , g(x) = 2ˣ. Compute f(g(x)).

x²
$log_2(x)$
2ˣ
x

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 »

$g(x)$ 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 11 Functions and Relations CCSS: HSF-BF.B.4b

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

$h(x) = x^2, ℝ$
h(x) = |x|, ℝ
$h(x) = x^4, ℝ$
h(x) = x², x ≥ 0

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

Given

$f(x) = (x - 5)/(x + 1)$ and

$g(x) = (-x - 5)/(x - 1)$ , is g = f⁻¹?

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

For

$f(x) = (x - 1)/(x + 4)$ and

$g(x) = (-4x - 1)/(x - 1)$ , verify if g = f⁻¹.

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

For

$f(x) = 5 - 3/(x+1)$ and

$g(x) = (3/(5-x)) - 1$ , verify inverse relationship.

True
False

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

f(x) = x⁴ (x ≥ 0), g(x) = √[4]{x}. Find f(g(x)).

|x|
$x^(1/4)$
x
x⁴

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

The inverse of

$f(x) = log_3(x - 1)$ is f⁻¹(x) = 3ˣ + 1.

True
False

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

$h(x)$ , 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 $x$ .

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

Find the inverse of g(x) = √(x - 3).

g⁻¹(x) = (x²) + 3
g⁻¹(x) = (x²) - 3
g⁻¹(x) = √(x + 3)
g⁻¹(x) = (x²)/3

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

Given

$f(x) = 4 + log_2(x-1)$ and

$g(x) = 2^(x-4) + 1$ , is g = f⁻¹?

True
False

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

For

$f(x) = 5 - e^(x+2)$ and g(x) = ln(5+x) - 2, verify if g = f⁻¹.

True
False

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

Let f(x) = 4x − 7 and

$g(x) = (x + 7)/4$ .
Compute g(f(x)). Is g the inverse of f?

x
x + 7
4x
x - 7

Share/Like This Page

Browse Questions

Common Core Standard HSF-BF.B.4b Questions

Become a Pro subscriber to access Common Core questions