Question

3. Evaluate at the given value: g(x)=-2x+7, g^-1(-2)​

Answer 1

-10

-12

Explanation:

Answer 2

`{g}^( - 1) ( - 2) = (9)/(2)`

Explanation:

To find g-¹( 2) we must first find g-¹(x)

To find g-¹(x) equate g(x) to y

That's

y = g(x)

We have

y = - 2x + 7

Now interchange the terms that's x becomes y and y becomes x

We have

x = - 2y + 7

Make y the subject in order to find g-¹(x)

Move 7 to the left side of the equation

- 2y = x - 7

Multiply both sides by - 1

We have

2y = 7 - x

Divide both sides by 2 to make y stand alone

That's

`y = (7 - x)/(2)`

So we have

`g ^( - 1) (x) = (7 - x)/(2)`

Now to find g-¹(- 2) substitute the value of x that's - 2 into the expression

We have

`{g}^( - 1) ( - 2) = (7 - - 2)/(2) \\ {g}^( - 1) ( - 2) = (7 + 2)/(2)`

We have the final answer as

`{g}^( - 1) ( - 2) = (9)/(2)`

Hope this helps you