Asked by Trish Goal
1. Let
f(x)=2x+5
g(x)=sqrt(f(x) -2
h(x)= f(g(x))
What is h(2)?
2. Define the function f(x)=2x-5. For what value of x is f(x) equal to f^-1(x)? Thanks!
f(x)=2x+5
g(x)=sqrt(f(x) -2
h(x)= f(g(x))
What is h(2)?
2. Define the function f(x)=2x-5. For what value of x is f(x) equal to f^-1(x)? Thanks!
Answers
Answered by
Steve
g(x) has unbalanced parentheses. I will assume you meant g(x) = √f(x) - 2
h(2) = f(g(2))
= f(√(f(2))-2)
= f(√(9)-2) = f(3-2) = f(1) = 7
f^-1(x) = (x+5)/2, so we need
2x-5 = (x+5)/2
4x-10 = x+5
3x = 15
x = 5
plug in x=5 for both functions to verify that it is correct.
h(2) = f(g(2))
= f(√(f(2))-2)
= f(√(9)-2) = f(3-2) = f(1) = 7
f^-1(x) = (x+5)/2, so we need
2x-5 = (x+5)/2
4x-10 = x+5
3x = 15
x = 5
plug in x=5 for both functions to verify that it is correct.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.