Question

If f (x) = 2x+5 and g (x) = x2 − 1 , then find i) (f ◦ g) (x) ii) (g ◦ f) (3)​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given :-

f(x) = 2x+5

g(x) = x²-1

To find :-

i) (f ◦ g) (x)

ii) (g ◦ f) (3)

Solution:-

Given that

f(x) = 2x+5

g(x) = x²-1

i) (f ◦ g) (x)

= f(g(x))

= f(x²-1)

= 2(x²-1)+5

= 2x²-2+5

= 2x²+3

Therefore, (f ◦ g) (x) = 2x²+3

ii) (g ◦ f) (x)

= g(f(x))

= g(2x+5)

= (2x+5)²-1

= (2x)²+2(2x)(5)+(5)²-1

= 4x²+20x+25-1

= 4x²+20x+24

Therefore, (g ◦ f) (x) = 4x²+20x+24

Now,(g ◦ f) (3)

= 4(3)²+20(3)+24

= 4(9)+60+24

= 36+60+24

= 120

or

(g ◦ f) (3)

= g(f(3))

= g(2(3)+5))

= g(6+5)

= g(11)

= 11²-1

= 121-1

= 120

Therefore, (g ◦ f) (3) = 120

Answer:-

i) (f ◦ g) (x) = 2x²+3

ii) (g ◦ f) (3) = 120