given the two functions f(x)=ln(4x - 1) and g...
given the two functions f(x)=ln(4x - 1) and g(x)=(x + 3)^2, calculate (f ∘ g)(32). round your final answer to two decimal places.
Answer
# Explanation:
## Step1: Calculate $g(32)$
Substitute $x = 32$ into $g(x)=(x + 3)^2$. So $g(32)=(32+3)^2=35^2 = 1225$.
## Step2: Calculate $(f\circ g)(32)$
Since $(f\circ g)(32)=f(g(32))$, and $g(32)=1225$, substitute $x = 1225$ into $f(x)=\ln(4x - 1)$. Then $f(1225)=\ln(4\times1225-1)=\ln(4900 - 1)=\ln(4899)$. Using a calculator, $\ln(4899)\approx8.59$.
# Answer:
$8.59$