Question

Which pairs of functions are inverses of each other? Choose all that are correct.

Answer 1

Its the second and third one

Answer 2

Answer:

C and D

Step-by-step explanation:

We have to find pairs of functions which are inverses of each other.

1.$f(x)=2x+3$ and $g(x)=0.5x-3$

Suppose y=f(x)

$y=2x+3$

$2x=y-3$

$x=\frac{y-3}{2}$

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

$f^{-1}(y)=\frac{y-3}{2}$

y replace by x

Then , we get

$f^{-1}(x)=\frac[x-3}{2}$

Hence, f(x) and g(x) are not inverses to each other.

B.$f(x)=\frac{1}{6}x-2$, and $g(x)=6x-12$

Suppose,$y=f(x)=\frac{1}{6}x-2$

$y+2=\frac{1}{6}x$

$6y+12=x$

Therefore,$f^{-1}(x)=6x+12$

Hence, f(x) and g(x) are not inverses to each other.

C.$f(x)=\frac{1}{3}x+5$ and $g(x)=3x-15$

Suppose ,$y=f(x)=\frac{1}{3}x+5$

$y-5=\frac{1}{3}x$

$3y-15=x$

Therefore, $f^{-1}(x)=3x-15=g(x)$

Hence, f(x) and g(x) are inverses of each other.

D.$f(x)=x^2+7$ and $g(x)=\pm \sqrt{x-7}$

Suppose , $y=f(x)=x^2+7$

$y-7=x^2$

$x=\pm \sqrt{x-7}$

Therefore, $f^{-1}(x)=\pm\sqrt{x-7}=g(x)$

Hence, f(x) and g(x) are inverses to each other.