Question

Match each function with its inverse function. use function composition to determine your answers.

Answer 1

QUESTION 1

$\boxed {f(x) = 2x + 6 \to \: g(x) = \frac{1}{2}x - 3 }$

The reason is that:

$g(f(x)) = 2( \frac{1}{2} x - 3) + 6$

Expand:

$g(f(x)) = x - 6+ 6$

$g(f(x)) = x$

QUESTION 2

$\boxed {f(x) =3 - 2x \to \: g(x) = - \frac{1}{2}(x - 3)}$

The reason that

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

$g(f(x)) = - \frac{1}{2} (- 2x )$

$g(f(x)) =x$

QUESTION 3

$\boxed {f(x) = \sqrt[3]{3x}+ 2 \to \: g(x) = \frac{ {(x - 3)}^{3} }{3} }$

The reason is that:

$f(g(x)) = \sqrt[3]{ \frac{3 {(x - 2)}^{3} }{3} } + 2$

$f(g(x)) = x-2 + 2$

$f(g(x))=x$

QUESTION 4

$\boxed {f(x)=3\sqrt[3]{x + 2} \to \: g(x) = \frac{1}{27} {x}^{3} - 2}$

The reason is that

$f(g(x)) = 3 \sqrt[3]{ \frac{1}{27} {x}^{3} - 2 + 2}$

$f(g(x)) = 3 \sqrt[3]{ \frac{1}{27} {x}^{3} }$

$f(g(x)) = 3 \times \frac{1}{3} x$

$f(g(x)) =x$