If F(x) and G(x) are two functions such that F(G(x)) = x then F(x) and G(x) are ..?

Mathematics

2 answers:

lana [24]3 years ago

4 0

They are inverse functions though to be completely thorough your teacher should have also put g(f(x)) = x as well. Though I can see what your teacher is aiming for at least.

The idea is that whatever the output of g(x) is, it's plugged into f(x) and the initial input is the result. So g(x) takes a step forward and f(x) takes a step back undoing everything g(x) did. Which is exactly what an inverse operation does.

olga_2 [115]3 years ago

3 0

If f(g(x))=x then they are inverse functions by definition

A is the answer

You might be interested in

Express 0.52 as a fraction

ioda

52/100
26/50
13/25
These will all do.

7 0

3 years ago

Read 2 more answers

A rectangle measures 6 3/4 cm by square root of 121 cm. What is the perimeter of the rectangle to the nearest tenth?

Anni [7]

Answer:

35.5 cm

Step-by-step explanation:

The perimeter (P) is calculated as

P = (2 × 6.75 ) + (2 × $\sqrt{121}$ )

= 13.5 + (2 × 11) = 13.5 + 22 = 35.5 cm

4 0

3 years ago

Read 2 more answers

What is the equation of a line perpendicular to:

Nataly [62]

Step-by-step explanation:

"perpendicular" means it creates a right angle (90°) with the original line.

a key element is the slope (the incline) of the line.

it is the factor of x (here 1/4 for the original line) and is defined as the ratio of "y coordinate change / x coordinate change" when going from one point on the line to another.

the given slope of 1/4 means that for every increase in x by 4 units y increases by 1 unit.

now if you want to draw a few random lines, and then draw lines that cross them with a right angle, you will see very quickly the relationship of the slopes of the crossing lines :

for the slope of the perpendicular line x and y of the original slope trade places (the ratio turns "upside-down") and the sign of the slope flips (if the original line goes up, then the perpendicular line goes down and vice versa. so + turns into -, and - into +).

so, our original slope 1/4 turns into -4/1 = -4.

we still have infinite possibilities to draw such a perpendicular line (more up or more down on the coordinate grid).

to finally "nail" one particular line we need to use the given point and solve for the y-intercept.

the general slope-intercept form is

y = ax + b

a is the slope, b is the y-intercept (the y value for x = 0).

so, using the slope (-4) and the point (2, 5) we have

5 = -4×2 + b = -8 + b

13 = b

so, the full equation is

y = -4x + 13

7 0