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Definition of Function

If fx = ax2...

Question

If $f (x) = (a x^{2} + b)^{3}$ then a function g(x) such that f(g(x)) = g (f(x)) is given by

g (x) = {(\frac{b - x^{1 / 3}}{a})}^{1 / 2}

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g (x) = \frac{1}{(a x^{2} + b)^{3}}

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g (x) = (a x^{2} + b)^{1 / 3}

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g (x) = {(\frac{x^{1 / 3} - b}{a})}^{1 / 2}

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Solution

The correct option is A $g (x) = {(\frac{b - x^{1 / 3}}{a})}^{1 / 2}$
Let $g (x)$ be $f^{- 1} x$ as $f (f^{- 1} (x)) = x$ and $f^{- 1} (f (x)) = x$

$\sqrt[3]{y} = a x^{2} + b \Rightarrow x^{2} =$ $\frac{\sqrt[3]{y} - b}{a}$

$x =$ ${(\frac{\sqrt[3]{y} - b}{a})}^{\frac{1}{2}}$

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Similar questions

If f(x)= $x^{\frac{1}{2}}, g (x) = x^{\frac{1}{3}} a n d h (x) = x^{\frac{2}{3}}$ . Find $\frac{f (x) + g (x)}{f (x) + h (x)}$

f (x) = a x^{2} + b x + c

g (x) = a x^{2} + p x + q

(b \neq q)

f (x) = g (x)

x = α

a \neq a_{1} \neq o

f (x) = a x^{2} + b x + C

g (x) = a_{1} x^{2} + b_{1} x + c_{1}

P (x) = f (x) - g (x)

P (x) = 0

x = - 1

p (- 2) = 2

P (2)

a \neq a_{1} \neq 0,

f (x) = a x^{2} + b x + c,

g (x) = a_{1} x^{2} + b_{1} x + c_{1}

p (x) = f (x) - g (x),

p (x) = 0

x = - 1

p (- 2) = 2

p (2)

If f(x)= $\frac{x^{1}}{2}$ , g(x)= $\frac{x^{1}}{3}$ and h(x)= $\frac{x^{2}}{3}$ . Find $\frac{(f + g) (x)}{(f + h) (x)}$

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