SOLUTION: Consider the function. F(x)=-7x+4 a.) Find the inverse of f(x) and g(x). Show and explain work b.) Draw the graphs of f(x) and g(x) on the same coordinate plan. Explain how your

Algebra ->  Graphs -> SOLUTION: Consider the function. F(x)=-7x+4 a.) Find the inverse of f(x) and g(x). Show and explain work b.) Draw the graphs of f(x) and g(x) on the same coordinate plan. Explain how your      Log On


   

Question 1002665: Consider the function. F(x)=-7x+4
a.) Find the inverse of f(x) and g(x). Show and explain work
b.) Draw the graphs of f(x) and g(x) on the same coordinate plan. Explain how your graph shows that the function are inverses of each other.
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
inverse is changing x and y then solving for y
y= -7x+4 becomes x=-7y+4
that is -7y=x-4
y=(-x/7)+(4/7)
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C-7x%2B4%2C%28-x%2F7%29%2B%284%2F7%29%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Consider the function. F%28x%29=-7x%2B4
a.) Find the inverse of f(x) and g(x). Show and explain work
recall that F%28x%29=y
so, you have y=-7x%2B4
to find inverse, first swap x and y
x=-7y%2B4...now solve for y which is going to be your g%28x%29
7y=-x%2B4
y=-%281%2F7%29x%2B4%2F7=> inverse g%28x%29=-%281%2F7%29x%2B4%2F7

b.) Draw the graphs of f(x) and g(x) on the same coordinate plan. Explain how your graph shows that the function are inverses of each other.
for each one you need two points to graph it
F%28x%29=-7x%2B4 find x and y-intercepts
0=-7x%2B4=>7x=4=>x=4%2F7=>x-intercept at (4%2F7,0)
F%28x%29=-7%2A0%2B4=>F%28x%29=+4=>y-intercept at (0,4)
g%28x%29=-%281%2F7%29x%2B4%2F7
0=-%281%2F7%29x%2B4%2F7=>x%2F7=4%2F7=>x=4=>x-intercept at (4,0)
F%28x%29=-%281%2F7%29%2A0%2B4%2F7=>F%28x%29=+4%2F7=>y-intercept at (0,4%2F7)
plot these points and draw a line through


Now I will plug the formula for f+%28x%29 into every instance of "x" in the formula for g%28x%29 :
g%28f%28x%29%29 if I end up with just "x", that will be proof that f+%28x%29 and g%28x%29 are inverses of each other
g%28-7x%2B4%29=-%281%2F7%29%2A%28-7x%2B4%29%2B4%2F7
g%28-7x%2B4%29=-%28-7x%2B4%29%2F7%2B4%2F7
g%28-7x%2B4%29=7x%2F7-4%2F7%2B4%2F7
g%28-7x%2B4%29=x-4%2F7%2B4%2F7
g%28-7x%2B4%29=x which proofs that f+%28x%29 and g%28x%29 are inverses of each other