Question

If f(x) = x2 − 1, and f(2a) = 35, then what could be the value of a ?
Answers;
-6
-3
1
2
6
Can somebody explain please?

Answer 1

Thank you.

Answer 2

\[f(x) = x^2-1\]That means to find the value of the function at any value of \(x\), we square \(x\) and subtract 1. If \(x = 2a\), we square \(2a\) and subtract 1:
\[f(2a) = (2a)^2-1 = 4a^2-1\]Now, we know that \(f(2a)=35\)so we can find the value of \(a\):
\[f(2a) = (2a)^2-1 = 4a^2-1=35\]\[4a^2-1+1=35+1\]\[4a^2=36\]\[a^2=9\]\[a=\pm3\]

Answer 3

Note that \(a=3\) would also be a valid answer, if it appeared in the list of answer choices.