Question

What is the value of y for f(x)= 2​

Answer 1

Answer and Step-by-step explanation:

To find the value of y for when f(x) is equal to 2, we need to replace f(x) with 2 and set it equal to the rest of the function.

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

First, add 2 to both sides.

`4 = ((1)/(2) )^(x)`

Now, we see that we end up with a 4 and a
`(1)/(2)`. If we plug -2 in for x, we see that it makes the fraction flip, so that the 2 is at the top and the 1 is at the bottom, and the -2 becomes positive 2 (this is done to keep an equation proper, since negative exponents aren't proper in an equation/expression).

`4 = (1^(-2) )/(2^(-2) ) \\\\\\4 = (2^2)/(1^2)\\\\\\4 = (4)/(1) \\\\\\4 = 4`

So, x = -2.

Now we plug -2 in for x to find the value of y.

f(x) =
`((1)/(2)) ^(-2) - 2`

f(x) = 4 - 2

f(x) = 2

y = 2

So, the value of y is 2.

You may be wondering, why did we do all that work just to get the same thing we were given?

Well, this is the explanation for getting the value of y. We plug in the value for f(x), and solve for x. Then we plug x in and solve for f(x), which is also y.

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