Question

Need this soon please -

Select the correct answer.
What is the inverse of function
f(x)=√x + 7

Answer 1

`\qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star`

• Option A is correct

`\textsf{ \underline{\underline{Steps to solve the problem} }:}`

Find inverse of given function :

`\qquad❖ \: \sf \:y = √(x) + 7`

`\qquad❖ \: \sf \: √(x) = y - 7`

`\qquad❖ \: \sf \:x = (y - 7) {}^(2)`

Next, replace x with f-¹(x) and y with x ~

`\qquad❖ \: \sf \:f {}^( - 1) (x) = (x - 7) {}^(2)`

we got our inverse function.

Condition : x should be greater or equal to 7

because we will get same value of y for different x if we also include values less than 7.

`\qquad \large \sf {Conclusion} :`

• Correct option is A

Answer 2

`\huge\mathbb{ \underline{SOLUTION :}}`

Given:

`\longrightarrow\bold{f(x)= √(7)}`

To solve for the inverse of a function we begin by re-writing the function as an equation in terms of y.

`\bold{Becomes,}`

Next step we switch sides for x and y variables and then solve for the y variable as shown below,

`\longrightarrow\sf{y= √(x)+7}`

`\bold{Then,}`

`\longrightarrow\sf{x= √(y)+7}`

`\small\bold{Solve \: for \: y \: and \: subtract \: 7 \: from \: the \: both \: }`
`\bold{sides,}`

`\longrightarrow\sf{x-7= √(y)}`

`\small\bold{Square \: both \: sides }`

`\sf{(x-7)^2=(√(y))^2}`

`\sf{(x-7)^2=y}`

We now re-write in function notation. Take note however that this is the inverse:

`\bold{Where \: y}`
`\sf{=(x-7)^2 }`

`\longrightarrow\sf{y= (x-7)^2 }`

`\huge\mathbb{ \underline{ANSWER:}}`

`\large\boxed{\sf A. \: \: f^(-1)(x)= (x − 7)^2 , \: for \: \underline > 7 }`