Question

if f(x)= 2x -1' g(x)=x+1\2 for all x€r find (gof) (x)

Answer 1

Hey There!!

Here we are given two functions:

$f(x)=2x-1 \\ \\ \\ g(x)=\frac{x+1}{2}$


We have to find gof(x). 


gof(x) is the composition of two functions. It can also be written as:

gof(x) = g(f(x))


This simply means that we put the value of f(x) in place of the x in g(x)

Here's what we do:


$gof(x) \\ \\ \\ = g(f(x)) \\ \\ \\ = g(\text{Put f(x) here}) \\ \\ \\ = g(2x-1) \\ \\ \\ = \frac{(2x-1) + 1}{2} \\ \\ \\ = \frac{2x}{2} \\ \\ \\ = x \\ \\ \\ \\ \implies \boxed{gof(x)=x}$


Thus, we have found the value of gof(x).


gof(x) = x



Hope it helps
Purva
Brainly Community

Answer 2

Step-by-step explanation:

Here we are given two functions:

\begin{gathered}f(x)=2x-1 \\ \\ \\ g(x)=\frac{x+1}{2}\end{gathered}

f(x)=2x−1

g(x)=

2

x+1

We have to find gof(x).

gof(x) is the composition of two functions. It can also be written as:

gof(x) = g(f(x))

This simply means that we put the value of f(x) in place of the x in g(x)

Here's what we do:

\begin{gathered}gof(x) \\ \\ \\ = g(f(x)) \\ \\ \\ = g(\text{Put f(x) here}) \\ \\ \\ = g(2x-1) \\ \\ \\ = \frac{(2x-1) + 1}{2} \\ \\ \\ = \frac{2x}{2} \\ \\ \\ = x \\ \\ \\ \\ \implies \boxed{gof(x)=x}\end{gathered}

gof(x)

=g(f(x))

=g(Put f(x) here)

=g(2x−1)

=

2

(2x−1)+1

=

2

2x

=x

⟹

gof(x)=x

Thus, we have found the value of gof(x).

gof(x) = x