If the function f(x) is defined for all real numbers x as the maximum

If f(x) is defined to be the greater of 2x + 4 and 12 + 3x, then (x) will equal 2x + 4 when 2x + 4 > 12 + 3x. Let’s solve this inequality:

2x + 4 > 12 + 3x

-x > 8

x < -8

Therefore, f(x) = 2x + 4 only when x is less than -8. The only answer choice which is less than -8 is E.

Answer: E

The maximum of two values is not the same as the greater one of those two values. Even two identical values have a maximum and a minimum.

Thus, f(x) = 2x + 4 if the following is true.

\(2x+4\geq 12+3x\)

\(-8\geq x\)

Only answer choice E satisfies the above condition for x.

Answer: E

Hi! I didn't understand the question stem:

"If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?"

How do you know that equation 1 >equation2?

Asked: If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?

(A) –4
2x+4= -8 + 4 = -4
12+3x= 12-12 = 0
f(x) = Max(2x+4,12+3x) = Max( -4,0 ) = 0
\(f(x) \neq 2x+4\)

(B) –5
2x+4= -10 + 4 = -6
12+3x= 12-15 = -3
f(x) = Max(2x+4,12+3x) = Max( -6,-3 ) = -3
\(f(x)\neq 2x+4\)

(C) –6
2x+4= -12 + 4 = -8
12+3x= 12-18 = -6
f(x) = Max(2x+4,12+3x) = Max( -8,-6 ) = -6
\(f(x) \neq 2x+4\)

(D) –7
2x+4= -14 + 4 = -10
12+3x= 12-21= -9
f(x) = Max(2x+4,12+3x) = Max( -10,-9 ) = -9
\(f(x) \neq 2x+4\)

(E) –9
2x+4= -18 + 4 = -14
12+3x= 12-27= -15
f(x) = Max(2x+4,12+3x) = Max( -14,-15 ) = -14
f(x) = 2x+4

IMO E

Asked: If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?

2x+4>12+3x
x<-8

x = -9 < -8

IMO E

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