Can you guide me how to solve Question 7b?

This is from iGCSE past examination paper. I could not even start.

Given that f(x) = 10^x.

(a) Calculate f(0.5).

(b) Write down the value of f^-1(1).

Usman

f^-1(x) is the inverse of function f.

Given that function f(x) = 10^x

So, f(1) = 10^1 = 10

f(2) = 10^2 = (10)(10) = 100 and so on

I think you can figure out 10^(0.5) ... it is the square root of ten, isn't it?

Let's get to 7(b), which is the one you wanted help in.

First you need to know the meaning of inverse of a function.

If a function is 2x (doubling a number) then its inverse is (1/2)x i.e. halving the number.

Given that f(x) = 10^x, the second part is asking you what is the value of x when f(x) = 1.

The answer is x = 0 because 10^0 = 1.

(Note: I use ^ to mean to the power of)

You may want to review the idea of inverse function.

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