If f(x)=5−4x2 and g(x)=23x−5, then (f∘g)(x)= ...
Explanation
Given the functions:
f(x)=5−4x2
g(x)=23x−5
We are asked to find the composition function (f∘g)(x).
By definition, (f∘g)(x)=f(g(x)). This means we substitute the entire function g(x) into the variable x in function f(x).
(f∘g)(x)=f(23x−5)=5−4(23x−5)2
Next, expand the squared fraction:
=5−4(22(3x−5)2)=5−4(49x2−30x+25)
Notice that the 4 in the numerator and denominator cancel out:
=5−(9x2−30x+25)
Distribute the negative sign:
=5−9x2+30x−25=−9x2+30x−20
Thus, (f∘g)(x)=−9x2+30x−20.