Question

For all values of x,
f(x)+x^2+3x and g(x)=x-4
show that fg(x)=x^2-5x+4

Answer 1

Step-by-step explanation:

g(x)= x-4

f(gx)= (x-4)²+3(x-4)

= x²+16-8x + 3x-12

= x²-5x+4

Answer 2

It has been proved that $\bf f(g(x)) = {x}^{2} - 5x + 4$

Given:

• Two functions.
• $f(x) = {x}^{2} + 3x$ and $g(x) = x - 4$

To find:

• Show that $f(g(x)) = {x}^{2} - 5x + 4$

Solution:

Concept to be used:

• Put x=g(x) in f(x).

Step 1:

Put x=g(x) in f(x).

In order to find fog, put the value of g(x) in place of x in f(x).

$f(g(x)) = ( {g(x)})^{2} + 3g(x)$

$\bf f(g(x)) = (x - 4)^{2} + 3(x - 4)$

Step 2:

Simplify the expression.

As,

$\bf ( {x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}$

$f(g(x)) = {x}^{2} - 8x + 16 + 3x - 12$

$\bf f(g(x)) = {x}^{2} - 5x + 4$

Hence proved.

Thus,

It has been proved that $\bf f(g(x)) = {x}^{2} - 5x + 4$

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