SOLUTION: Find the inverse of the function, if it exists. Justify if is does not. 1.p(x)=3x+8 2.f(x)=x²+2x - 1 3.g(x)=2x+7 4.f(x)=x³ - 5 5.h(x)=x+2/2x - 3

Algebra ->  Testmodule -> SOLUTION: Find the inverse of the function, if it exists. Justify if is does not. 1.p(x)=3x+8 2.f(x)=x²+2x - 1 3.g(x)=2x+7 4.f(x)=x³ - 5 5.h(x)=x+2/2x - 3      Log On


   

Question 1186178: Find the inverse of the function, if it exists. Justify if is does not.
1.p(x)=3x+8
2.f(x)=x²+2x - 1
3.g(x)=2x+7
4.f(x)=x³ - 5
5.h(x)=x+2/2x - 3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find the inverse of the function, if it exists. Justify if is does not.
1. p%28x%29=3x%2B8
p%28x%29=y
y=3x%2B8......swap variables
x=3y%2B8...solve for y
x-8=3y+
y=%28x-8%29%2F3
=>p'%28x%29=%28x-8%29%2F3


2. f%28x%29=x%5E2%2B2x+-+1
y=x%5E2%2B2x+-+1.....swap variables
x=y%5E2%2B2y+-+1
x%2B1=y%5E2%2B2y ...complete square
x%2B1=%28y%5E2%2B2y%2Bb%5E2%29-b%5E2.........b=1
x%2B1=%28y%2B1%29%5E2-1%5E2
x%2B1%2B1=%28y%2B1%29%5E2+
%28y%2B1%29%5E2=x%2B2
y%2B1=srt%28x%2B2%29
y=-1 ± sqrt%28x+%2B+2%29
f'%28x%29=-1 ± sqrt%28x+%2B+2%29


3. g%28x%29=2x%2B7
y=2x%2B7.....swap variables
x=2y%2B7
2y=x-7
y=%28x-7%29%2F2
g'%28x%29=%28x-7%29%2F2


4.f%28x%29=x%5E3+-+5
y=x%5E3+-5...swap variables
x=y%5E3+-+5
x%2B5=y%5E3
y=root%283%2Cx%2B5%29
f'%28x%29=root%283%2Cx%2B5%29


5.h%28x%29=%28x%2B2%29%2F%282x-3%29
y=%28x%2B2%29%2F%282x-3%29...swap variables
x=%28y%2B2%29%2F%282y+-+3%29
x%282y+-+3%29=%28y%2B2%29
2xy+-+3x=y%2B2
2xy+-+y=3x%2B2
%282x+-+1%29y=3x%2B2
y=%283x%2B2%29%2F%282x+-+1%29
h'%28x%29=%283x%2B2%29%2F%282x+-+1%29