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

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4 votes

Answer:

The answer is


√(2) \: \: or \: \: 1.414

Explanation:


h(x) = {2}^(x)

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

To find h-¹(x) equate h(x) to y

That's


y = {2}^(x)

Next interchange the terms

x becomes y and y becomes x

That's


{2}^(y) = x

Make y the subject

Take logarithm to base 2 to both sides

That's


log_(2)( {2} )^(y) = log_(2)x \\ y log_(2)2 = log_(2)(x)

But


log_(2)(2) = 1


y = log_(2)(x)

So we have


{h}^( - 1) (x) = log_(2)(x)

Now we can solve the equation

We have


log_(2)(x) = 0.5

Convert the logarithm into exponential form using the fact that


log_(a)(x) = b \: \: \cong \: \: x = {a}^(b)

So we have


x = {2}^(0.5)

But


{2}^(0.5) = √(2)

So we have the final answer as


√(2) \: \: or \: \: 1.414

Hope this helps you

User Netadictos
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