If f(x) = x2 − 1, and f(2a) = 35, then what could be the value of a ?
f(2a)=35
35=(2a)^2-1
35=4a^2-1
minus 35 from both sidse
0=4a^2-36
facor out 4
0=4(a^2-9)
factor differece of 2 perfect squares
0=4(a-3)(a+3)
set to zero
a-3=0
a=3
a+3=0
a=-3
a=-3 or 3
The values of a function are gotten from the input variables
The values of a could be 3 or -3
We have:
\(f(x) = x^2 - 1\)
Substitute 2a for x
\(f(2a) = (2a)^2 - 1\)
Expand
\(f(2a) = 4a^2 - 1\)
Substitute 35 for f(2a)
\(f(2a) = 4a^2 - 1 =35\)
So, we have:
\(4a^2 - 1 =35\)
Add 1 to both sides
\(4a^2 =35+1\)
\(4a^2 =36\)
Divide both sides by 4
\(a^2 = 9\)
Take square roots
\(a = \±3\)
Hence, the values of a could be 3 or -3
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