Mathematics
Algebra 2 test needs all work shown

### Question Description

if f(x)=x to the third power -ax 8 and f to the negative 1 power(52)=4 find the value of a

So with the caveat that it's not clear what "-ax 8" is... presumably there should be an operator between the x and the 8?

The key is to understand what f^-1(x) is, the inverse function of x. It's very simple - if f(x) = some expression involving x, then given a value for x, you can find f(x). f^-1(x) just works in reverse (being the inverse function). If you know the value for f(x), and plug it in to the f^-1(x) inverse function, it will spit out the original value of x.

So, you don't actually need to know what f^-1(x) is. You're told that f^-1(52) = 4. That means that for f(x)=52, you have x = 4.

So just substitute these into your original equation for f(x). I'm going to assume the missing operator is a +, but it will be easy for you to adjust this if it's something else:

f(x) = x^3 - ax + 8

52 = (4)^3 - 4a + 8

52 = 64 - 4a + 8

4a = 20

a = 5

Hope this was helpful!

iainharlow (1041)
Boston College
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