Trigonometry: Expression to Fraction

Question

Write the expression as a single fraction: 3 sec(-x) +2.

Explain in detailed steps.

Answer 1

3sec(-x) + 2 = 3secx + 2 = 3(1/cosx) + 2 = (3 + 2cosx) / cosx

Answer 2

f(x) = 3sec(-x) +2

cosines and secants are even trig functions, such that f(-x) = f(x), so

f(x) = 3sec(-x)+2

= 3secx +2

it's f(x) = secx transformed by stretching vertically with a factor of 3 and a vertical shift up by 2

the domain is all real numbers, but the range is all real numbers except 5 < f(x) < -1

3sec180+2 < f(x) < 3sec0+2 are values not in the range

if you want a "single fraction" just put it all over 1

(3secx +2)/1