Question

Which of the following statements have the same result? Explain each step in solving each one.

f(1) when f(x) = 5x + 1
f−1(3) when f(x) = 2x plus 3, all over 5
3y − 7 = y + 5

Answer 1

`f(x) = 5x + 1\\\\subtitute\ x = 1\ to\ the\ equation\\\\f(1) = 5\cdot1 + 1 = 5 + 1 = 6\\----------------------\\f(x)=(2x+3)/(5)\to y=(2x+3)/(5)\ \ \ \ |multiply\ both\ sides\ by\ 5\\\\5y=2x+3\ \ \ \ |subtract\ 3\ from\ both\ sides\\\\2x=5y-3\ \ \ \ \ |divide\ both\ sides\ by\ 2\\\\x=(5y-3)/(2)\\\\f^(-1)(x)=(5\cdot(-1)-3)/(2)=(-5-3)/(2)=(-8)/(2)=-4\\---------------------\\3y-7=y+5\ \ \ |add\ 7\ to\ both\ sides\\3y=y+12\ \ \ \ |subtract\ y\ from\ both\ sides\\2y=12\ \ \ \ |divide\ both\ sides\ by\ 2\\y=6`

Answer: f(1) when f(x) = 5x + 1 and 3y - 7 = y + 5