A function f is defined by f(x) = 2x - 3. By writing the full working, write the values of (a) f(0) (b) f(-2) (c) f(3) (d) f(-1)

1 answer:

6 0

A) f(x) = 2x - 3
f(0) = 2(0) - 3
f(0) = 0 - 3
f(0) = -3

b) f(x) = 2x - 3
f(-2) = 2(-2) - 3
f(-2) = -4 - 3
f(-2) = -7

c) f(x) = 2x - 3
f(3) = 2(3) - 3
f(3) = 6 - 3
f(3) = 3

d) f(x) = 2x - 3
f(-1) = 2(-1) - 3
f(-1) = -2 - 3
f(-1) = -5

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Please help :)))) ( attachment )

Anastaziya [24]

Let,
f(x) = -2x+34
g(x) = (-x/3) - 10
h(x) = -|3x|
k(x) = (x-2)^2

This is a trial and error type of problem (aka "guess and check"). There are 24 combinations to try out for each problem, so it might take a while. It turns out that

g(h(k(f(15)))) = -6
f(k(g(h(8)))) = 2

So the order for part A should be: f, k, h, g
The order for part B should be: h, g, k f
note how I'm working from the right and moving left (working inside and moving out).

Here's proof of both claims

-----------------------------------------

Proof of Claim 1:

f(x) = -2x+34
f(15) = -2(15)+34
f(15) = 4
-----------------
k(x) = (x-2)^2
k(f(15)) = (f(15)-2)^2
k(f(15)) = (4-2)^2
k(f(15)) = 4
-----------------
h(x) = -|3x|
h(k(f(15))) = -|3*k(f(15))|
h(k(f(15))) = -|3*4|
h(k(f(15))) = -12
-----------------
g(x) = (-x/3) - 10
g(h(k(f(15))) ) = (-h(k(f(15))) /3) - 10
g(h(k(f(15))) ) = (-(-12) /3) - 10
g(h(k(f(15))) ) = -6

-----------------------------------------

Proof of Claim 2:

h(x) = -|3x|
h(8) = -|3*8|
h(8) = -24
---------------
g(x) = (-x/3) - 10
g(h(8)) = (-h(8)/3) - 10
g(h(8)) = (-(-24)/3) - 10
g(h(8)) = -2
---------------
k(x) = (x-2)^2
k(g(h(8))) = (g(h(8))-2)^2
k(g(h(8))) = (-2-2)^2
k(g(h(8))) = 16
---------------
f(x) = -2x+34
f(k(g(h(8))) ) = -2*(k(g(h(8))) )+34
f(k(g(h(8))) ) = -2*(16)+34
f(k(g(h(8))) ) = 2

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3 years ago

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Multiply within the parentheses

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Add inside the parenthesis:

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Multiply:

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The answer is -39

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