Question

If the function h is defined by h(x)=lign="absmiddle" class="latex-formula">-3x+5,then h(2x+1)=

Answer 1

Given:

The function is:

$h(x)=x^2-3x+5$

To find:

The value of $h(2x+1)$.

Solution:

We have,

$h(x)=x^2-3x+5$

Putting $x=2x+1$, we get

$h(2x+1)=(2x+1)^2-3(2x+1)+5$

$h(2x+1)=(2x)^2+2(2x)(1)+(1)^2-3(2x)-3(1)+5$

$h(2x+1)=4x^2+4x+1-6x-3+5$

On combining like terms, we get

$h(2x+1)=4x^2+(4x-6x)+(1-3+5)$

$h(2x+1)=4x^2-2x+3$

Therefore, the required function is $h(2x+1)=4x^2-2x+3$.