Given f(x) = 2x^2 – 2 and g(x) = –2x + 4, find the following.
(f − g)(2)
AND
Given f(x) = 2x − 2 and g(x) = 4x − 5, evaluate the composite function.
f[g(2)]
(f-g)(2) = f(2) - g(2)
= 2*2^2-2 - (-2*2+4)
= 6 - 0
= 6
f(g(2) = 2*g(2) - 2
= 2(4*2-5)-2
= 2*3-2
= 4
To find (f - g)(2), we need to substitute x = 2 into both f(x) and g(x) and then subtract the results.
First, let's find f(2) by substituting x = 2 into f(x) = 2x^2 - 2:
f(2) = 2(2)^2 - 2
= 2(4) - 2
= 8 - 2
= 6
Next, let's find g(2) by substituting x = 2 into g(x) = -2x + 4:
g(2) = -2(2) + 4
= -4 + 4
= 0
Finally, we can calculate (f - g)(2) by subtracting f(2) from g(2):
(f - g)(2) = f(2) - g(2)
= 6 - 0
= 6
Therefore, (f - g)(2) = 6.
Now, let's evaluate the composite function f[g(2)].
First, let's find g(2) by substituting x = 2 into g(x) = 4x - 5:
g(2) = 4(2) - 5
= 8 - 5
= 3
Now that we know g(2) = 3, we can substitute it into f(x) = 2x - 2:
f[g(2)] = f(3)
= 2(3) - 2
= 6 - 2
= 4
Therefore, f[g(2)] = 4.