Question 1002665
Consider the function. {{{F(x)=-7x+4}}}
a.) Find the inverse of f(x) and g(x). Show and explain work

recall that {{{F(x)=y}}}
so, you have {{{y=-7x+4}}}
to find inverse, first swap {{{x}}} and {{{y}}}

{{{x=-7y+4}}}...now solve for {{{y}}} which is going to be your {{{g(x)}}}

{{{7y=-x+4}}}

{{{y=-(1/7)x+4/7}}}=> inverse {{{g(x)=-(1/7)x+4/7}}}
 
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(x)=-7x+4}}} find x and y-intercepts

{{{0=-7x+4}}}=>{{{7x=4}}}=>{{{x=4/7}}}=>x-intercept at ({{{4/7}}},{{{0}}})
{{{F(x)=-7*0+4}}}=>{{{F(x)= 4}}}=>y-intercept at ({{{0}}},{{{4}}})

{{{g(x)=-(1/7)x+4/7}}}

{{{0=-(1/7)x+4/7}}}=>{{{x/7=4/7}}}=>{{{x=4}}}=>x-intercept at ({{{4}}},{{{0}}})
{{{F(x)=-(1/7)*0+4/7}}}=>{{{F(x)= 4/7}}}=>y-intercept at ({{{0}}},{{{4/7}}})

plot these points and draw a line through


 {{{drawing( 600, 600, -10, 10, -10, 10,
circle(4/7,0,.12),circle(0,4,.12),
locate(4/7,0,p(4/7,0)),locate(0,4,p(0,4)),

circle(4,0,.12),circle(0,4/7,.12),
locate(4,0,p(4,0)),locate(0,4/7,p(0,4/7)),
 graph( 600, 600, -10, 10, -10, 10, -7x+4, -(1/7)x+4/7)) }}}

Now I will plug  the formula for {{{f (x)}}} into every instance of "x" in the formula for {{{g(x)}}} :

{{{g(f(x))}}} if  I end up with just "{{{x}}}", that will be proof that  {{{f (x)}}} and {{{g(x)}}} are inverses of each other

{{{g(-7x+4)=-(1/7)*(-7x+4)+4/7}}} 

{{{g(-7x+4)=-(-7x+4)/7+4/7}}} 

{{{g(-7x+4)=7x/7-4/7+4/7}}} 

{{{g(-7x+4)=x-4/7+4/7}}}

{{{g(-7x+4)=x}}} which proofs that  {{{f (x)}}} and {{{g(x)}}} are inverses of each other