Question

Let f : R → R : f(x) = 2x + 5 and g : R → R : g(x) = x2 + x.
Find
(i) (f + g) (x)
(ii) (f – g) (x)

Answer 1

Question:

Let f : R → R : f(x) = 2x + 5 and g : R → R : g(x) = x2 + x.

Find

(i) (f + g) (x)

(ii) (f – g) (x)

$\:$

Step-by-step explanation:

(i) To find:

• (f + g) (x)

(f + g) (x) = f(x) + g(x)

= (2x + 5) + (x^2 + x)

= 2^x + 5 + x^2 + x

= x^2 + 3x + 5

Therefore,

(f + g) (x) = x2 + 3x + 5

$\:$

(ii) To find:

• (f - g) (x)

(f - g) (x) = f(x) - g(x)

= (2x + 5) - (x2 + x)

$\sf \: = 2x + 5 - x^2- x \\ \sf= -x^2 + x + 5$

Therefore,

(f + g) (x) = $\sf-x^2 + x + 5$

$\large \cal{Q} \frak{ian} \cal{N} \frak{iu}$