Question

Find the maximum and minimum values of - |x - 2| + 5
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Answer 1

(i)f(x)=∣x−2∣−1

Minimum value of ∣x−2∣=0

Minimum value of f(x)=minimum value of ∣x−2∣−1

=0−1=−1

Minimum value of f(x)=−1→(x=−2)

f(x) has no maximum value.

(ii)f(x)=−∣x+1∣+3

∣x+1∣>0

⇒−∣x+1∣<0

Maximum value of g(x)=maximum value of −∣x+1∣+3

=0+3=3

Maximum value of g(x)=3

There is no minimum value of g(x