F(x)=2x+3,a=-1 find 1/f. And graph f and 1/f?

Answer 1

Given the function f(x) = 2x + 3 and a = -1, we can find f(a) as follows:

f(a) = 2(-1) + 3

f(a) = -2 + 3

f(a) = 1

So, f(a) = 1.

To graph f(x) and 1/f(x), we can plot several points and connect them to visualize the functions. Here are some points for f(x):

For f(x):

When x = -2, f(x) = 2(-2) + 3 = -1

When x = -1, f(x) = 2(-1) + 3 = 1

When x = 0, f(x) = 2(0) + 3 = 3

When x = 1, f(x) = 2(1) + 3 = 5

When x = 2, f(x) = 2(2) + 3 = 7

Now, to find 1/f(x), we take the reciprocal of each f(x) value:

For 1/f(x):

When x = -2, 1/f(x) = 1/(-1) = -1

When x = -1, 1/f(x) = 1/1 = 1

When x = 0, 1/f(x) = 1/3 ≈ 0.333

When x = 1, 1/f(x) = 1/5 ≈ 0.2

When x = 2, 1/f(x) = 1/7 ≈ 0.143

Now, we can plot these points and connect them to obtain the graphs of f(x) and 1/f(x).