Given:
The function is:
[tex]h(x)=x^2-3x+5[/tex]
To find:
The value of [tex]h(2x+1)[/tex].
Solution:
We have,
[tex]h(x)=x^2-3x+5[/tex]
Putting [tex]x=2x+1[/tex], we get
[tex]h(2x+1)=(2x+1)^2-3(2x+1)+5[/tex]
[tex]h(2x+1)=(2x)^2+2(2x)(1)+(1)^2-3(2x)-3(1)+5[/tex]
[tex]h(2x+1)=4x^2+4x+1-6x-3+5[/tex]
On combining like terms, we get
[tex]h(2x+1)=4x^2+(4x-6x)+(1-3+5)[/tex]
[tex]h(2x+1)=4x^2-2x+3[/tex]
Therefore, the required function is [tex]h(2x+1)=4x^2-2x+3[/tex].
