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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).
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