1. ## Solve Equations

Hi there,

Can someone please solve 3 equations for me, i am confused how to solve these. Thanks for your help

1)
Solve the two sided inequality and show the solution on real line
7 < 1-2x ≤ 10

2)
Given two functions as:
f(x) = and g(x) =
Find fog(x) also find the domain of f, g and fog

2. Originally Posted by accmaster
Hi there,

Can someone please solve 3 equations for me, i am confused how to solve these. Thanks for your help

1)
Solve the two sided inequality and show the solution on real line
7 < 1-2x ≤ 10
Treat the inequality like any other equation.

$7< 1-2x \leq 10$

Subtract 1 from all parts:

$7 - 1< 1-2x - 1 \leq 10 - 1$

$6< -2x \leq 9$

And remember that when you divide or multiply by a negative number, the sign flips around.

Try finish this.

2)
Given two functions as:
f(x) = and g(x) =
Find fog(x) also find the domain of f, g and fog
Sorry, the functions are not appearing.

Anyway, if f(x) = x + 1 and g(x) = 3x - 1, then

fog(x) = f(3x -1) = (3x - 1) + 1 = 3x

From there, you should have an idea of the shapes of all the three functions, and give their domain.