Question

If f (x)= 3x+5, g(x) =6x_1 then find (f+g)(x) 2》(f-g) (2)
3》(fg) (3)
4》(f/g) (x) and it domain

Answer 1

Answer:

a) (f + g)(x) = 9x + 4, (b) (f - g)(2) = 0, (c) (fg)(x) = 18x^2+27x-5=18x

2

+27x−5

(d) (\dfrac{f}{g} )(

g

f

) (x) =\dfrac{3x+5}{6x-1}=

6x−1

3x+5

and Domain = Set of all real numbers except \dfrac{1}{6}

6

1

.

Step-by-step explanation:

Given,

f(x) = 3x + 5, g (x) = 6x - 1

To find, (a) (f + g)(x) (b) (f-g) (2) (c) (tg) (3) (d) (\dfrac{f}{g} )(

g

f

) (x) and its domain.

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

= 3x + 5 + 6x - 1

= 9x + 4

(b) (f - g)(2)

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

= 3x + 5 - 6x + 1

= - 3x + 6

∴ f(2) + g(2)

= - 3(2) + 6

= - 6 + 6

= 0

(c) (fg)(x) = f(x).g(x)

= (3x + 5)(6x - 1)

= 18x^2-3x+30x-5=18x

2

−3x+30x−5

= 18x^2+27x-5=18x

2

+27x−5

(d) (\dfrac{f}{g})(x)=\dfrac{f(x)}{g(x)}(

g

f

)(x)=

g(x)

f(x)

=\dfrac{3x+5}{6x-1}=

6x−1

3x+5

For domain,

6x - 1 ≠ 0

6x ≠ 1

x ≠ \dfrac{1}{6}

6

1

Domain = Set of all real numbers except \dfrac{1}{6}

6

1

.