Question

If the function 'a' is$x^3$. which of the following could be the function b?

• A. $x^{\frac{1}{3}}$
• B. x+$x^3$
• C. $x^{\frac{1}{5}}$
• D. $x^3$+$x^{\frac{1}{3}}$

Answer 1

The correct option is A

$x^{\frac{1}{3}}$

We are given the function a is $x^3$. The line between them is the graph of y = x. the graph 'b' looks like the mirror image of a about y = x.

This means the function g(x) of graph b is the inverse function of $x^3$.

It means g( $x^3$) = 1 or $\left(g\right(x){)}^3$= 1. Only one option out of the four satisfies this condition.

We can find the inverse function in the following way. If f(x) is the inverse of g(x), to find g(x) when f(x) is given, write

y = f(x)

After this step, try to find x in terms of y. replace y with x in this expression. That will be the function g(x).

For example, to find the inverse of $x^3$,

y = $x^3$

$\Rightarrow$ x =$y^{\frac{1}{3}}$

Now in $y^{\frac{1}{3}}$ we replace y with x to get the inverse.

$\Rightarrow$$x^{\frac{1}{3}}$ is the inverse.