SOLUTION: If f(x)=3x+1, u(x)=square root x, and h(x)=1/(x+1), find h(f(u(x)).

Algebra ->  Functions -> SOLUTION: If f(x)=3x+1, u(x)=square root x, and h(x)=1/(x+1), find h(f(u(x)).       Log On


   

Question 177006: If f(x)=3x+1, u(x)=square root x, and h(x)=1/(x+1), find h(f(u(x)).
Found 2 solutions by Fombitz, rapaljer:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's go step by step.
f%28x%29=3x%2B1
u%28x%29=sqrt%28x%29
h%28x%29=1%2F%28x%2B1%29
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.
.
f%28u%28x%29%29=3%28sqrt%28x%29%29%2B1
f%28u%28x%29%29=3%2Asqrt%28x%29%2B1
.
.
.
h%28f%28u%28x%29%29%29=1%2F%28%283%2Asqrt%28x%29%2B1%29%2B1%29
h%28f%28u%28x%29%29%29=1%2F%283%2Asqrt%28x%29%2B2%29

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Given f(x)=3x+1, u(x)=square root x, and h(x)=1/(x+1), find h(f(u(x)).

First,
f(x)=3x+1, u(x)=sqrt%28x%29, so to find f(u(x)) substitute the u(x) into the formula for f(x) like this: f(u(x))= 3sqrt%28x%29+1.

Next, h(f(u(x))), substitute f(u(x)) into the formula for h(x) like this:
h%28x%29+=+1%2F%28x%2B1%29
h%28f%28u%28x%29%29%29+=+1%2F%28%283%2Asqrt%28x%29+%2B+1+%29+%2B1%29
h%28f%28u%28x%29%29%29+=+1%2F%283%2Asqrt%28x%29+%2B+2%29
R^2