H(x) = 2^x
Solve the equation h^-1 (x) =0.5

The answer is

Step-by-step explanation:

To solve the equation we must first find h-¹(x)

To find h-¹(x) equate h(x) to y

That's

Next interchange the terms

x becomes y and y becomes x

That's

Make y the subject

Take logarithm to base 2 to both sides

That's

But

So we have

Now we can solve the equation

We have

Convert the logarithm into exponential form using the fact that

So we have

But

So we have the final answer as

Hope this helps you

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step-by-step explanation:

sorry no step by step