Suppose the functions f(x) and g(x) are inverse functions.About what line is the graph of g(x) a reflection

Mathematics

2 answers:

nalin [4]3 years ago

8 0

If f(x) and g(x) are inverse functions, their graphs are reflections of one another in the line y=x.

jolli1 [7]3 years ago

3 0

If two functions are inverse of each other, they are basically switching the x- and y-axes.

Take for example, p(x)=2x, is a line passing through the origin with a slope of two. Its inverse, q(x)=x/2, is a line passing through the origin with a slope of 1/2, the reciprocal of 2. If you plot the two lines, you will notice that the two lines are symmetrical about y=x, or a 45 degree line from the x-axis.

This also explains y=x (which lines on the line of reflection) has its inverse also equal to y=x!

You might be interested in

1. There are two differnt maps of Ohio. The scale on the first map is 1 cm to 10 km. The distance from Cleveland to Cincinnati i

xeze [42]

Answer:

1. 0.8 cm

2. 1.6 cm

Step-by-step explanation:

The scale for 2nd map is 1 cm to 50 km, that means "1 cm on map" is "50 km in real life".

We already know distance from Cleveland to Cincinnati is 40 km, which is less than 50, so we know the distance on map would be less than 1 cm.

So we set up ratio and figure out (let x be distance on map from Cleveland to Cincinnati):

$\frac{1}{50}=\frac{x}{40}\\50x=40\\x=\frac{40}{50}\\x=0.8$