Verify Functions Are Inverses
Algebra 2 · Flashcards
ALGEBRA 2 · FLASHCARDS
Card 1
of 51
0 got it
0 to review
Current
Got it
Still learning
Not seen
QUESTION
What is
f
(
g
(
x
)
)
f(g(x))
f
(
g
(
x
))
if
f
(
x
)
=
x
f(x)=\sqrt{x}
f
(
x
)
=
x
and
g
(
x
)
=
x
2
g(x)=x^2
g
(
x
)
=
x
2
with domain
x
≥
0
x\ge 0
x
≥
0
for
g
g
g
?
QUESTION
What is the key simplification goal when checking
f
(
g
(
x
)
)
f(g(x))
f
(
g
(
x
))
to verify inverses?
QUESTION
What is
g
(
f
(
x
)
)
g(f(x))
g
(
f
(
x
))
if
f
(
x
)
=
x
3
+
1
f(x)=x^3+1
f
(
x
)
=
x
3
+
1
and
g
(
x
)
=
x
−
1
3
g(x)=\sqrt[3]{x-1}
g
(
x
)
=
3
x
−
1
?
Tap to flip before you grade
ANSWER
g
(
f
(
x
)
)
=
x
g(f(x))=x
g
(
f
(
x
))
=
x
. Substituting:
g
(
x
3
+
1
)
=
(
x
3
+
1
)
−
1
3
=
x
g(x^3+1)=\sqrt[3]{(x^3+1)-1}=x
g
(
x
3
+
1
)
=
3
(
x
3
+
1
)
−
1
=
x
.
Swipe → got it · swipe ← still learning
Got it
Still learning
Flip Card
Previous card
Next card