Answer:
Part 1) No
Part 2) Option 4. [tex]f^{-1}(x)=-\frac{1}{3}x+3[/tex]
part 3) [tex]f^{-1}(9)=4[/tex]
Step-by-step explanation:
Part 1) we have
[tex]f(x)=8x-3[/tex]
[tex]g(x)=(x+8)/3[/tex] Â
Find the inverse of f(x) and then compare with g(x)
Let
y=f(x)
[tex]y=8x-3[/tex]
Exchange the variables x for y and y for x
[tex]x=8y-3[/tex]
Isolate the variable y
[tex]8y=(x+3)[/tex]
[tex]y=(x+3)/8[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=(x+3)/8[/tex]
therefore
the functions f(x) and g(x) are not inverses of each other
Part 2) we have
[tex]f(x)=-3x+9[/tex]
Let
y=f(x)
[tex]y=-3x+9[/tex]
Exchange the variables x for y and y for x
[tex]x=-3y+9[/tex]
Isolate the variable y
[tex]3y=-x+9[/tex]
[tex]y=(-x+9)/3[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=(-x+9)/3[/tex]
[tex]f^{-1}(x)=-\frac{1}{3}x+3[/tex]
Part 3) we know that
For [tex]x=4[/tex], [tex]f(x)=9[/tex]
so
For [tex]x=9[/tex], [tex]f^{-1}(9)=4[/tex]
