Question

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

Answer 1

Answer:

${g}^{ - 1} ( - 2) = \frac{9}{2}$

Step-by-step 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

$y = \frac{7 - x}{2}$

So we have

$g ^{ - 1} (x) = \frac{7 - x}{2}$

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

We have

${g}^{ - 1} ( - 2) = \frac{7 - - 2}{2} \\ {g}^{ - 1} ( - 2) = \frac{7 + 2}{2}$

We have the final answer as

${g}^{ - 1} ( - 2) = \frac{9}{2}$

Hope this helps you