All categories

3 years ago

Evaluate fog and gof if f(x)=5x-8 and g(x)= x^3

Mathematics

1 answer:

DerKrebs [107]3 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

note that f ○ g = f(g(x))

To evaluate substitute x = x³ into f(x)

f(g(x)) = f(x³) = 5x³ - 8

In the same way

g ○ f = g(f(x))

To evaluate substitute x = 5x - 8 into g(x)

g(f(x)) = g(5x - 8) = (5x - 8)³

You might be interested in

Will markk the brainliest

ivolga24 [154]

Answer:

1. the range of f^-1(x) is {10, 20, 30}.

2. the graph of f^-1(x) will include the point (0, 3)

3. n = 8

Step-by-step explanation:

1. The domain of a function is the range of its inverse, and vice versa. The range of f^-1(x) is {10, 20, 30}.

2. See above. The domain and range are swapped between a function and its inverse. That means function point (3, 0) will correspond to inverse function point (0, 3).

3. The n-th term of an arithmetic sequence is given by ...

an = a1 +d(n -1)

You are given a1 = 2, a12 = 211, so ...

211 = 2 + d(12 -1)

209/11 = d = 19 . . . . . solve the above equation for the common difference

Now, we can use the same equation to find n for an = 135.

135 = 2 + 19(n -1)

133/19 = n -1 . . . . . . . subtract 2, divide by 19

7 +1 = n = 8 . . . . . . . . add 1

135 is the 8th term of the sequence.

3 0

3 years ago

Simplifying an Expression with the Numerator and the Denominator Raised to a Power

slamgirl [31]

Answer:

The answer to your question is the second option $\frac{1}{x^{48}y^{36}z^{6}}$

Step-by-step explanation:

Expression

$[\frac{(x^{2}y^{3})^{-2}}{(x^{6}y^{3}z)^{2}}]^{3}$

Process

1.- Divide the fraction in numerator and denominator

a) Numerator

[(x²y³)⁻²]³ = (x⁻⁴y⁻⁶)³ = x⁻¹²y⁻¹⁸

b) Denominator

[(x⁶y³z)²]²= (x¹²y⁶z²)³ = x³⁶y¹⁸z⁶

2.- Simplify like terms

a) x⁻¹²x⁻³⁶ = x⁻⁴⁸

b) y⁻¹⁸y⁻¹⁸= y⁻³⁶

c) z⁻⁶

3.- Write the fraction

$\frac{1}{x^{48}y^{36}z^{6}}$

6 0

2 years ago

PLEASE HELP, ILL GIVE BRAINLIEST! SIMPLE MATHS.

dusya [7]

The answer is c i’m pretty sure

7 0

2 years ago

Read 2 more answers

B. Create an equation and sketch a graph that:

aev [14]

Answer:

Step-by-step explanation:

Yes.

3 0

2 years ago

Read 2 more answers

The lines below are perpendicular if the slope of the solid line is 4 what is the slope of the dashed line

const2013 [10]

Answer:

The slope of the dashed line is $-\frac{1}{4}$

Step-by-step explanation:

Perpendicular lines and slopes:

If two lines are perpendicular, the multiplication of their slopes is -1.

What is the slope of the dashed line

Perpendicular to a line with slope 4, so:

$4m = -1$

$m = -\frac{1}{4}$

The slope of the dashed line is $-\frac{1}{4}$

8 0

2 years ago