please help?

1)f(f^-1(x)=x ,rule
5f^-1(x) )-7 =x
F^-1(x)=(x+7)/5
f^-(-27) =(-27+7)/5=-20/5=-4
2) f^-1(x) =(x-2)/3
3)g^-1(x)=x+4
f(g(x))=f(x-4)=5(x-4) -7=5x-20-7=5x-27

1 find the inverse function. Show all steps.
f(x) = 5x – 7 Then find f ^ -1 (-27)

Let y = 5x - 7

Solve for x

y + 7 = 5x

x = (y + 7)/5

swap x and y

y = (x + 7)/5

so f^-1(x) = (x + 7)/5

f^-1(-27) = (-27 + 7)/5

= -20/5

= - 4


2 f(x) = 3x + 2 g(x) = x – 4 find (fg)(x) and simplify. please show your work

Does fg(x) stand for f*g(x) or fog(x)

I am assuming it is fog(x) = f(g(x))

fg(x) = f(g(x))

= f(x - 4)

= 3(x - 4) + 2

= 3x - 12 + 2

= 3x - 10

Or

f*g(x) = (3x + 2)(x - 4)

= 3x^2 - 12x + 2x - 8

= 3x^2 - 10x - 8

1. y = 5x -7
x = 5y -7
x + 7/5 = 5y/5
y =( x + 7) / 5

y = (-27 +7) / 5
y = -4

2. (3x + 2)(x - 4)
= 3x^2 - 12x + 2x -8
= 3x^2 -10x -8

1.
Let y = f(x) = 5x - 7 and g (y) = x
g is inverse of f

5x = y + 7
x = [ y + 7 ] / 5
g (y) = [ y + 7 ] / 5
g (x) = [ x + 7 ] / 5

2.
f [ g(x) ] = f [ x - 4 ] = 5x - 27