Questions: Determine whether the two functions are inverses. f(x)=5x+4 and g(x)=(x-4)/5

Determine whether the two functions are inverses. f(x)=5x+4 and g(x)=(x-4)/5
Transcript text: Determine whether the two functions are inverses. \[ f(x)=5 x+4 \text { and } g(x)=\frac{x-4}{5} \]
failed

Solution

failed
failed

Solution Steps

Step 1: Determine the Composition \( f(g(x)) \)

To determine if two functions are inverses, we need to check if their compositions result in the identity function. First, we find \( f(g(x)) \).

Given: \[ f(x) = 5x + 4 \] \[ g(x) = \frac{x-4}{5} \]

Substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f\left(\frac{x-4}{5}\right) = 5\left(\frac{x-4}{5}\right) + 4 \]

Simplify: \[ = x - 4 + 4 = x \]

Step 2: Determine the Composition \( g(f(x)) \)

Next, we find \( g(f(x)) \).

Substitute \( f(x) \) into \( g(x) \): \[ g(f(x)) = g(5x + 4) = \frac{(5x + 4) - 4}{5} \]

Simplify: \[ = \frac{5x}{5} = x \]

Step 3: Conclusion

Since both compositions \( f(g(x)) = x \) and \( g(f(x)) = x \), the functions \( f(x) \) and \( g(x) \) are indeed inverses of each other.

Final Answer

\[ \boxed{\text{The two functions are inverses.}} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Salem Amusement Park paid 180,000 for a concession stand. Salem started out depreciating the building using the straight-line method over 10 years with a residual value of zero. After using the concession stand for six years, Salem determines that the building will remain useful for only two more years. Record Salem's depreciation on the concession stand for year seven using the straight-line method. (Record debits first, then credits. Exclude explanations from any journal entries.)
failedAnswered
Suppose your school costs for this term were 8040 and financial aid covered 3/4 of that amount. How much did financial aid cover? How much do you still have to pay?
failedAnswered
Under certain conditions the rate of this reaction is zero order in dinitrogen monoxide with a rate constant of 0.0059 M · s^-1: 2 N2O(g) → 2 N2(g) + O2(g) Suppose a 3.0 L flask is charged under these conditions with 400 mmol of dinitrogen monoxide. After how much time is there only 200 mmol left? You may assume no other reaction is important. Be sure your answer has a unit symbol, if necessary, and round it to the correct number of significant digits.
failedAnswered
A ship carrying 1000 passengers is wrecked on a small island from which the passengers are never rescued. The natural resources of the island restrict the population to a limiting value of 5740, to which the population gets closer and closer but which it never reaches. The population of the island after time t, in years, is approximated by the logistic equation given below, Complete parts (a) through (c). P(t) = 5740 / (1 + 4.74 e^(-0.4 t)) a) Find the population after 15 years. (Round to the nearest integer as needed.)
failedAnswered
2. Civilizations in the Americas A. were culturally and linguistically diverse. B. developed writing at the same time. C. communicated in the same language. D. didn't have organized religion.