VIPSolutionsy SRmSEmEREE a EE HA NAHAHH | HA EEE SAHA EEENEERG NEY A HA FE EE Ep i NEANGER7ZE NE HE: HEATH InEERNaEEEET EEEEE ENE HEmEEREEaETT THEREEEEEERTT a — — —— Evaluate each expression using the graphs of y= f(x) and y = g(x) shown below. @(@en-1) ®)(geno) ©og=1) (@(Fe9)4) RRR RE Pe EERE EE @(en(-1=[] | (Simplify your answer.) ©) (9000 =["] (Simplify your answer.) ©ooN-n=[] (Simplify your answer.) @ (fe q@=[] (Simplify your answer.)
Question:
y
SRmSEmEREE
a EE
HA NAHAHH
| HA
EEE SAHA
EEENEERG NEY A
HA
FE EE Ep
i NEANGER7ZE NE HE:
HEATH
InEERNaEEEET
EEEEE ENE
HEmEEREEaETT
THEREEEEEERTT
a — — ——
Evaluate each expression using the graphs of y= f(x) and y = g(x) shown below.
@(@en-1) ®)(geno) ©og=1) (@(Fe9)4)
RRR RE Pe EERE EE
@(en(-1=[]
| (Simplify your answer.)
©) (9000 =["]
(Simplify your answer.)
©ooN-n=[]
(Simplify your answer.)
@ (fe q@=[]
(Simplify your answer.)
This is AI generated Response.
Asked by: Venkatesh
Created at: 2025-09-01 16:49:07
Asked by: Venkatesh
Created at: 2025-09-01 16:49:07
Final Answer:
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Let’s solve each part step by step using the graphs for \( f(x) \) and \( g(x) \):
---
### (a) \( (g \circ f)(-1) \)
This means \( g(f(-1)) \).
1. Find \( f(-1) \) from the graph of \( y = f(x) \):
- At \( x = -1 \), \( f(x) = -2 \).
2. Now find \( g(-2) \) from the graph of \( y = g(x) \):
- At \( x = -2 \), \( g(x) = 5 \).
**Answer:**
\[
(g \circ f)(-1) = g(f(-1)) = g(-2) = 5
\]
---
### (b) \( (g \circ f)(0) \)
This means \( g(f(0)) \).
1. Find \( f(0) \) from the graph of \( y = f(x) \):
- At \( x = 0 \), \( f(x) = -3 \).
2. Now find \( g(-3) \) from the graph of \( y = g(x) \):
- At \( x = -3 \), \( g(x) = 6 \).
**Answer:**
\[
(g \circ f)(0) = g(f(0)) = g(-3) = 6
\]
---
### (c) \( (f \circ g)(-1) \)
This means \( f(g(-1)) \).
1. Find \( g(-1) \) from the graph of \( y = g(x) \):
- At \( x = -1 \), \( g(x) = 7 \).
2. Now find \( f(7) \) from the graph of \( y = f(x) \):
- At \( x = 7 \), \( f(x) = 3 \).
**Answer:**
\[
(f \circ g)(-1) = f(g(-1)) = f(7) = 3
\]
---
### (d) \( (f \circ g)(4) \)
This means \( f(g(4)) \).
1. Find \( g(4) \) from the graph of \( y = g(x) \):
- At \( x = 4 \), \( g(x) = 3 \).
2. Now find \( f(3) \) from the graph of \( y = f(x) \):
- At \( x = 3 \), \( f(x) = 1 \).
**Answer:**
\[
(f \circ g)(4) = f(g(4)) = f(3) = 1
\]
---
### **Summary**
- (a) \( (g \circ f)(-1) = 5 \)
- (b) \( (g \circ f)(0) = 6 \)
- (c) \( (f \circ g)(-1) = 3 \)
- (d) \( (f \circ g)(4) = 1 \)
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