Question

In: Advanced Math

Suppose f is a function deﬁned for all real numbers which has a maximum value of...

Suppose f is a function deﬁned for all real numbers which has a maximum value of 5 and a minimum value of −7. Label each of the following as MUST, MIGHT, or NEVER true. Explain, and if you say might, give an example of yes and an example of no.

A The maximum value of f(|x|) is 7.

B The maximum value of f(|x|) is 5.

C The maximum value of f(|x|) is 0.

D The minimum value of f(|x|) is 7.

E The minimum value of f(|x|) is 5.

F The minimum value of f(|x|) is 0.

G The maximum value of |f(x)| is 7.

H The maximum value of |f(x)| is 5.

I The maximum value of |f(x)| is 0.

J The minimum value of |f(x)| is 7.

K The minimum value of |f(x)| is 5.

L The minimum value of |f(x)| is 0.

Now suppose f is a continuous function deﬁned for all real numbers which has a maximum value of 5 and a minimum value of −7. Which of the answers above stay the same (why?), and which change (to what, and why?)

Solutions

Expert Solution

(A) NEVER

(B) MIGHT

(C) MIGHT

(D) NEVER

(E) MIGHT

(F) MIGHT

(G) ALWAYS

(H) NEVER

(I) NEVER

(J) NEVER

(K) MIGHT

(L) MIGHT

All of the above answers remain the same as each of the above examples can be redefined using intervals so that f(x) becomes continuous.

For example, the last function in (L) can be redefined as

The properties will remain the same.

Colby Messinger answered 1 year ago

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