Question

Let f(x) = 2x + 1 and g(x) = x^2+x-2

find (fg)(x) =

Answer 1

`\huge \boxed{ \boxed{\sf {2x}^(2) + 2x - 6} }`

Explanation:

to understand this

you need to know about:

• composite function
• PEMDAS

tips and formulas:

• 
  `(f \circ \: g)x \iff \: f(g(x))`

given:

• f(x)=2x+1
• g(x)=x²+x-2

let's solve:

1. 
   `\sf sustitute \: the \: value \: of \: g(x) \: to \: f(x) : \\ \sf2( {x}^(2) + x - 2) - 2`
2. 
   `\sf distribute : \\ \sf 2 {x}^(2) + 2x - 4 - 2`
3. 
   `\sf simplify \: substraction : \\ \sf {2x}^(2) + 2x - 6`

Answer 2

Solution given:

(x) = 2x + 1

and

g(x) = x^2+x-2

now

fg (x)=f( x^2+x-2)= 2( x^2+x-2) + 1=2x²+2x-4+1

=2x²+2x-3 is your answer