Answer :
Answer:
Step-by-step explanation:
(f∘g)(x) = f(g(x))
= f(x²-3)
= 2(x²-3) + 1
= 2x² - 5
(f∘g)(-2) = 2(-2)² - 5
= 2·4 - 5
= 8 - 5
= 3
The composition (f ∘ g)(–2) for the functions f(x) = 2x + 1 and g(x) = x2 – 3 will be 3
What is composition of a function ?
The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)). It means here function g is applied to the function of x. So, basically, a function is applied to the result of another function.
The notation used for composition is: (f o g)(x) = f(g(x))
(fog)(x) = f(g(x))
this implies , (fog)(-2) = f(g(2))
given :
f(x) = 2x + 1
g(x) = x2 – 3
(fog)(x) = f(g(x)) = f(x^2 - 3)
= 2 (x^2 -3) +1
= 2x^2 - 5 equation 1
fog(-2) = f(g(2))
substituting the value of x = 2 in equation 2
= 2 * (2)^2 -5
= 3
learn more about composition of a function :
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