Question

H(x) = −(x − 5)2 + 3

Answer 1

Max(f(x)) = f(3) = 4

Max(g(x)) = g(π/2) = 2

Max(h(x)) = h(5) = 3

Of these values, f(3) = 4 is the largest.


The function with the largest maximum is f(x).

Answer 2

Answer:

The correct option is 1. The function f(x) has the largest maximum.

Step-by-step explanation:

The vertex form of a parabola is

$y=a(x-h)^2+k$

Where, (h,k) is vertex.

The given functions is

$h(x)=-(x-5)^2+3$

Here, a=-1, h=-5 and k=3. Since the value of a is negative, therefore it is an downward parabola and vertex is the point of maxima.

Thus the maximum value of the function h(x) is 3.

$g(x)=4\cos (2x-\pi)-2$

The value of cosine function lies between -1 to 1.

$-1\leq \cos (2x-\pi)\leq 1$

Multiply 4 on each side.

$-4\leq 4\cos (2x-\pi)\leq 4$

Subtract 2 from each side.

$-4-2\leq 4\cos (2x-\pi)-2\leq 4-2$

$-6\leq 4\cos (2x-\pi)-2\leq 2$

Therefore the maximum value of the function g(x) is 2.

From the given table it is clear that the maximum value of the function f(x) is 4 at x=3.

Since the function f(x) has the largest maximum, therefore the correct option is 1.