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GaryK [48]
3 years ago
7

Find f(g(-4)) and g(f(-4)) using the functions below. f(x) = 2x + 7 g(x) = x2 + 3x - 1

Mathematics
1 answer:
daser333 [38]3 years ago
8 0

Answer:

f(g(-4)) = 13.

g(f(-4)) = -3.

Step-by-step explanation:

g(-4) = (-4)^2 + 3(-4) - 1

= 3.

so f(g(-4))

= f(3)

= 2(3) + 7

= 13.

f(-4) =  2(-4) + 7

= -1.

so g (f(-4))

= g(-1)

= (-1)^2 - 3 - 1

= -3.

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Three consecutive odd integers have a sum of 27. Find the integers.
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\sf \bf {\boxed {\mathbb {GIVEN:}}}

Sum of three consecutive odd integers = 27

\sf \bf {\boxed {\mathbb {TO\:FIND:}}}

The values of the three integers.

\sf \bf {\boxed {\mathbb {SOLUTION:}}}

\sf\purple{The\:three\:consecutive \:odd\:integers\:are\:7,\:9\:and\:11.}

\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}

Let us assume the three consecutive odd integers to be x, (x+2) and (x+4).

As per the condition, we have

Sum \:  \:  of \:  \:  the  \:  \: three \:  \:  consecutive \:  \:  odd \:  \:  integers  = 27

➺ \: x + (x + 2) + (x + 4) = 27

➺ \: x + x + 2 + x + 4 = 27

Now, collect the like terms.

➺ \: (x + x + x) + (2 + 4) = 27

➺ \: 3x + 6 = 27

➺ \: 3x = 27 - 6

➺ \: 3x = 21

➺ \: x =  \frac{21}{3} \\

➺ \: x = 7

Therefore, the three consecutive odd integers whose sum is 27 are \boxed{  7  }, \boxed{ 9   } and \boxed{ 11   } respectively.

\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}

⇢ 7 + 9 + 11 = 27

⇢ 27 = 27

⇢ L. H. S. = R. H. S.

\sf\blue{Hence\:verified.}

\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}

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