Question

In Exercise 13, solve y=f(x) for x. Then find the input when the output is 2.

13. f(x) = 9x^2

I don't understand how to solve this question. I know the answer, but can you lead me through the steps you took to solve the problem? Thanks!

Answer 1

x = ±(√y)/3

x = ±(√2)/3

Explanation:

Put the given information in the given equation and solve for x:

f(x) = 2

2 = 9x^2 . . . . . use 2 in place of f(x)

2/9 = x^2 . . . . divide by 9

±√(2/9) = x . . . take the square root

x = ±(√2)/3 . . . simplify

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Using this as an example, we can solve f(x) = y in the same way:

y = 9x^2 . . . . use y for f(x)

y/9 = x^2 . . . divide by the coefficient of x^2

±√(y/9) = x . . . take the square root; next, simplify

x = ±(√y)/3 . . . . the equation solved for x. Note this matches the above when y=2.