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
Answers
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
.