Question

Suppose that the functions u and w

u(x)=x^2+5
w(x)=sqrtx+7
Find the following.

(u o w)(2)
(w o u)(2)

Answer 1

what is \(w(2)\) ?

Answer 2

@ganeshie8 can you help with this?

Answer 3

\(\large (u~o~w)(2)\)

is same as

\(\large u( ~w(2)~)\)

Answer 4

start by finding \(w(2)\)

Answer 5

\(\large w(x)=\sqrt{x+7}\)


\(\large w(2) = ?\)

Answer 6

are you saying to substitute x for 2 then evaluate?

Answer 7

yup !

Answer 8

\[w(x)=\sqrt{2+7}\]

Answer 9

simplify

Answer 10

\[=\sqrt{9}=3\]

Answer 11

yes !

Answer 12

\(\large (u~o~w)(2) = u(~w(2)~)\)

\(\large ~~~~~~~~~ ~~~~~~~= u(~3~)\)

\(\large ~~~~~~~~~~~~~~~~~ = ?\)

Answer 13

so now I am substituting 3 for x?

Answer 14

yes,
u do that in u(x) ok ?

Answer 15

14?

Answer 16

\(\large (u~o~w)(2) = u(~w(2)~)\)

\(\large ~~~~~~~~~ = u(~3~)\)

\(\large ~~~~~~~~~ = 3^2+5 = 14\)

Answer 17

14 is right !

Answer 18

see if u can find the second one : (w o u)(2)

Answer 19

4?

Answer 20

You got it !

Answer 21

good job :)