Let g be the function defined by g(t) = t^2 − 5

Question

Find all the values of t such that g(t) = 7

Answer 1

To find all values of t for which g(t) = 7, set the given equation for g(t) equal to 7

g(t) = t² - 5

7 = t² - 5

t² - 12 = 0

(t + √12)(t - √12) = 0

t = - √12 t = √12

So, there are 2 possible values of t for which g(t) = 7, { -√12, +√12}

Answer 2

g(t) = t^2 - 5. when g(t) = 7. therefore:-

t^2 -5 = 7 add 5 to both sides

t^2 -5 + 5 = 7 + 5

t^2 = 12 square root both sides to get rid of the square (^2)

t = 2√3,−2√3 or 3.4641, -3.4641