Question

Evaluate following two compositions:
a: (f ° g) (x)
b: (h° g) (x)

f(x) = 2x+5;
g(x) = x^2-3;
h(x) = (7-x)/(3)

Answer 1

f ((7-x)/(3) ) by definition

(f°h)(x) = ((7-x)/(3) )^2 -3

Answer 2

\[(f ° h)(x) = (\frac{ 7-x }{ 3 } )^{2}-3\]

Answer 3

h (g(x)) by definition

h (x^2-3)

Answer 4

\[(h ° g)(x) = \frac{ 7-x ^{2}-3 }{ 3} \]

Answer 5

(-x^2+4)/(3)

Answer 6

@iPwnBunnies

Answer 7

a: (f ° g) (x) = f( g(x) )
f(x) = 2x+5; g(x) = x^2-3.
f( g(x) ) = 2(x^2-3) + 5 = 2x^2 - 6 + 5 = 2x^2 - 1

Answer 8

A = (f ° g)(x) = f(g(x)) by definition

\[f(x ^{2}-3)\]

\[2(x ^{2}-3) +5\]

Answer 9

\[(f ° g)(x) = 2x ^ {2} -6 +5 -->2x ^{2}-1\]

Answer 10

correct. Do the next one the same way. b: (h° g) (x)

Answer 11

b: (h° g) (x) = h( g(x) )

g(x) = x^2-3; h(x) = (7-x)/(3)

(h° g) (x) = h( g(x) ) = h( x^2-3 ) = ( 7 - (x^2-3) ) / 3 = (7 - x^2 + 3) / 3 = (10-x^2)/3

Answer 12

b: (h°g)(x) = h(g(x)) by definition

h(x^2-3)

\[\frac{ 7-(x ^{2}-3) }{ 3 } = \frac{ 10-x ^{2} }{ 3 }\]

Answer 13

correct.

Answer 14

THanks a lot, you have been helpfull

Answer 15

you are welcome.

Answer 16

\[h(x ^{2}-3)\]

Answer 17

\[f ^{-1}(x) = 2y +5\]

Answer 18

x= 2y + 5
-5 +x = 2y

Answer 19

\[-\frac{ 5 }{ 2 }+\frac{ x }{ 2 } = y\]

Answer 20

\[f ^{-1}(x) = \frac{ x }{ 2 }- \frac{ 5 }{ 2 }\]

Answer 21

\[h ^{-1}(x) =\]

Answer 22

\[x = \frac{ 7-y }{ 3 }\]

Answer 23

\[3x=7-y\]

Answer 24

\[3x-7=-y\]

Answer 25

\[-3x+7 = y\]

Answer 26

\[h ^{-1}(x) = -3x+7\]

Answer 27

\[(2x+5)- (\frac{ 7-x }{ 3 }) = 2x+5 -\frac{ 7 }{ 3 }+\frac{ x }{3 }\]