Question

What is the answer to this question?

Answer 1

`\boxed{\pink{\sf Option \ (1) \ is \ correct . }}`

Explanation:

Given function to us is ,

`\implies y = 5x^2 + 10`

And, we need to find the inverse of the equation.

So , for that firstly replace x with y . The equation becomes

`\implies x = 5y^2 + 10`

Now , next we need to solve for y .

`\implies x = 5y^2 + 10 \\\\\implies 5y^2 = x - 10 \\\\ \implies y^2 = (x-10)/(5) \\\\\implies y = \sqrt{(x-10)/(5)}`

Now , replace y for
`f^(-1)(x)`

`\underline{\boxed{\orange{\tt \implies f^(-1)(x) = \pm\sqrt{(x-10)/(5)}}}}`

As per the options provided in Question we can that option (1) mathces with our answer when we just interchanged the variables.

Hence option (1) is correct.