Does any1 know the answers for this?
2 answers:
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The value of the function f(g) after simplifying and putting 2 in place of <em>x</em> is -20 and the value of f(g(2)) is 418.
<h3>What is composite function?</h3>When a function is written inside the another function, then such function is called the composite function.
The first function given in the problem is,
The second function given,
To find out the value of g(2), put the 2 on place of variable x in the above equation as,
The composite function f(g(x)) can be given as,
Thus, the value of the function f(g) after simplifying and putting 2 in place of <em>x</em> is -20 and the value of f(g(2)) is 418.
Learn more about the composite function here:
Answer:
Formula for g(x) is
Step-by-step explanation:
Given - g is a trigonometric function of the form g(x)=a sin (bx+c)+d. The function intersects its midline at (-1 , 6) and has a minimum point at (-3.5 , 3)
To find - Find a formula for g (x). Give an exact expression.
Proof -
Given that,
g(x)=a sin (bx+c)+d
We know that, Midline is present in between maximum and minimum
Here given that, minimum is present is 3 and midline is present at 6
So, Maximum occurs at 9.
Now,
We know that,
Standard form of sine function is - g(x) = Asin(B(x-C)) + D
Where
A = Amplitude
and Amplitude = (Maximum - minimum) / 2
= (9 - 3)/ 2
= 6/2 = 3
⇒A = 3
Now,
Period =
⇒B = (2π) / Period
= (2π) / 10
= π/5
⇒B = π/5
Now,
Phase Shift : C = -1 ( i.e. 1 to the left)
Vertical Shift : D = 6
So,
We get
g(x) = Asin(B(x-C)) + D
=
⇒
∴ we get
Formula for g(x) is
