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stealth61 [152]
3 years ago
14

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

Mathematics
1 answer:
topjm [15]3 years ago
6 0

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

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